Implicit time integration for plasma simulation

We apply the second-order formulation of Maxwell's equations proposed by Jiang et al. (1996, J. Comput. Phys. 125, 104) to the solution of the implicit formulation of the three-dimensional, time-dependent Vlasov-Maxwell's system. An implicit finite difference algorithm is developed to solve the Maxwell's equations in a bounded domain with physical boundary conditions comprising electrically conducting walls (perfect conductors) and constant magnetic flux walls. We formulate the boundary conditions for Maxwell's equations to satisfy Poisson's equation throughout the domain by solving it only on the boundary. This eliminates the need for a separate projection step. We compare numerical results with analytical solutions for electromagnetic waves in vacuo, and using the implicit particle-in-cell code CELESTE3D, we test the new solver on the geospace environment modeling magnetic reconnection challenge problem. c 2002 Elsevier Science (USA)

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“…The role of θ in energy conservation is discussed in [9]. Filtering for higher order time differencing is discussed in [15,47].…”

Section: Temporal Discretizationmentioning

confidence: 99%

A Simplified Implicit Maxwell Solver

Ricci

Lapenta

Brackbill

2002

Journal of Computational Physics

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“…Of course, this generally translates into the requirement for large computational resources. Historically, the search for more efficient PIC schemes based on implicit time discretization dates back to the 1980s, when the implicit moment [55][56][57] and the direct implicit [58,59] methods were introduced. Both methods rely on a linearization of the equations for the electromagnetic fields, and, thus, they should be more properly regarded as semi-implicit methods.…”

Section: Introductionmentioning

confidence: 99%

On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

Camporeale

Delzanno

Bergen

et al. 2016

Computer Physics Communications

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a b s t r a c tWe describe a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Lapenta (2011) andChen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier-Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC.

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“…There are basically two classes of implicit PIC methods : the direct implicit method [8,31] and the implicit moment method [33,34]. In the direct implicit method, an implicit algorithm for the advancement of the particles is introduced.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic-Preserving Particle-In-Cell method for the Vlasov–Poisson system near quasineutrality

Degond

Deluzet

Navoret

et al. 2010

Journal of Computational Physics

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This paper deals with the numerical resolution of the Vlasov-Poisson system in a nearly quasineutral regime by Particle-In-Cell (PIC) methods. In this regime, classical PIC methods are subject to stability constraints on the time and space steps related to the small Debye length and large plasma frequency. Here, we propose an "Asymptotic-Preserving" PIC scheme which is not subject to these limitations. Additionally, when the plasma period and Debye length are small compared to the time and space steps, this method provides a consistent PIC discretization of the quasineutral Vlasov equation. We perform several one-dimensional numerical experiments which provide a solid validation of the method and its underlying concepts, and compare the method with classical PIC and Direct-Implicit methods.

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Implicit time integration for plasma simulation

Cited by 117 publications

References 6 publications

A Simplified Implicit Maxwell Solver

A Simplified Implicit Maxwell Solver

On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

Asymptotic-Preserving Particle-In-Cell method for the Vlasov–Poisson system near quasineutrality

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